This is a pretty colloquial British phrase. With the exception of a small group of Red Dwarf fans, I don't think the average American would get this reference. I'm assuming he means it literally, as in "I'll be right back." But I can imagine, if a situation is difficult or dangerous, it could also be used as expression of confidence. Sort of an "I can do this!" expression.

In the United Kingdom, Isle of Man, Japan, and a minority of North American regions kippers, or smoked herring are often eaten for breakfast. https://en.wikipedia.org/wiki/Kipper So, his slogan "Smoke me a kipper, I'll be back for breakfast." is a kind of joke, I suppose.